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%I #11 Apr 25 2018 10:42:55
%S 2,33,65,96,244,307,730,761,972,1025,1088,1753,3126,3189,3854,4097,
%T 4128,4339,5120,7221,7777,7840,8505,11872,15626,15657,15868,16649,
%U 16808,16871,17536,18750,20903,23401,32432,32769,32832,33497,36864,46657,46688,46899,47680,48393
%N Numbers of the form a^5 + b^6, with integers a, b > 0.
%C Although it is easy to produce many terms of this sequence, it is nontrivial to check whether a very large number is of this form.
%C This sequence is among others motivated by the hard-to-compute sequence A300567 = numbers z such that z^7 = x^5 + y^6 for some x, y >= 1.
%o (PARI) is(n,k=5,m=6)=for(b=1,sqrtnint(n-1,m),ispower(n-b^m,n)&&return(b)) \\ Returns b > 0 if n is in the sequence, else 0.
%o A303375_vec(L=10^5,k=5,m=6,S=List())={for(a=1,sqrtnint(L-1,m),for(b=1,sqrtnint(L-a^m,k), listput(S,a^m+b^k)));Set(S)} \\ all terms up to limit L
%Y Cf. A000404 (a^2 + b^2), A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4).
%Y Cf. A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6).
%Y See also A300567: numbers z such that z^7 = x^5 + y^6 for some x, y >= 1.
%K nonn,easy
%O 1,1
%A _M. F. Hasler_, Apr 22 2018
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